60 lines
1.2 KiB
Markdown
60 lines
1.2 KiB
Markdown
---
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id: 5900f53e1000cf542c510051
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title: 'Problem 466: Distinct terms in a multiplication table'
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challengeType: 5
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forumTopicId: 302141
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dashedName: problem-466-distinct-terms-in-a-multiplication-table
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---
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# --description--
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Let $P(m,n)$ be the number of distinct terms in an $m×n$ multiplication table.
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For example, a 3×4 multiplication table looks like this:
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$$\begin{array}{c}
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× & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} \\\\
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\mathbf{1} & 1 & 2 & 3 & 4 \\\\
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\mathbf{2} & 2 & 4 & 6 & 8 \\\\
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\mathbf{3} & 3 & 6 & 9 & 12
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\end{array}$$
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There are 8 distinct terms {1, 2, 3, 4, 6, 8, 9, 12}, therefore $P(3, 4) = 8$.
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You are given that:
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$$\begin{align}
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& P(64, 64) = 1\\,263, \\\\
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& P(12, 345) = 1\\,998, \text{ and} \\\\
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& P(32, {10}^{15}) = 13\\,826\\,382\\,602\\,124\\,302. \\\\
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\end{align}$$
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Find $P(64, {10}^{16})$.
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# --hints--
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`multiplicationTable()` should return `258381958195474750`.
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```js
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assert.strictEqual(multiplicationTable(), 258381958195474750);
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```
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# --seed--
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## --seed-contents--
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```js
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function multiplicationTable() {
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return true;
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}
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multiplicationTable();
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```
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# --solutions--
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```js
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// solution required
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```
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